Does using a credit card actually build up your credit score or do you have to incur charges by not paying it off for X amount of time to help with your credit rating?
No. Absolutely, unequivocally NO. Anyone who says that is lying or repeating "conventional wisdom".
If I'm paying it off every month and using it for everything I buy, am I doing myself a disservice?
It depends on the ratio between the card balance's and the card's credit limit.
For example, if the credit limit is $12,000 and the balance is $3,000 then the "usage rate" is $3K/$12K = 25%.
Conventional wisdom is that any usage rate over 30% reduces your score, but have never seen confirmation from the scoring agencies.
I use my card for almost everything, and pay zero interest even though it's a high rate card. To keep the usage rate low, (and because it simplifies my monthly cash flow), I pay my card multiple times per month so that the usage rate on the bill is less than 2%.